Wednesday, February 27, 2008

Forthcoming attractions ...

And what happened to my "blogview" of Absolute Generality? Good question! I've been a bit snowed under. But I plan to get back to that -- at long last -- next week, finishing looking at the papers in the book, preparatory to writing an overdue review for BSL. Then I plan to discuss chapter by chapter Charles Parsons' new Mathematical Thought and Its Objects, for which I'm going to be writing a critical notice for Analysis Reviews (the successor to Philosophical Books).

So I hope there'll shortly be a bit more substantive content here again. Watch this space!

Gödel corrections/exercises

I'm updating the list of errors/infelicities in my Gödel book which I've been told about or have found myself. Thanks to those of you who both spotted typos and took the trouble to tell me about them! -- and especial thanks to Peter Milne for spotting the one silly but substantive error that I'd overlooked, and to Tim Button and Bruno Whittle for discussions which I hope have led to some suggested improvements to the very last argument in the book. I hope the proposed corrections will all get made in a second printing of the book.

I've been a bit daunted by the self-imposed task of adding some exercises on the website to accompany the book, and -- given the pressure of other work -- I had rather ground to a halt. But I'll have to get back to this, even if I only add stuff piecemeal as I think of new things, not worrying at all if for quite a while the spread of exercises remains patchy and idiosyncratic. I hope to start adding some exercises to the site in the coming few weeks.

Sunday, February 24, 2008

Cost benefit analysis

One paper, read to the Jowett Society, Oxford.

Costs. A day and a half putting the talk together (relatively quick, as the talk was about Church's Thesis, which I've written about before in my Gödel book, and here on the blog), and then a couple of hours making Beamer slides for the data projector. Travel over to Oxford (never enjoyable, whichever way you go from Cambridge). Giving the talk (always anxiety making). Not me at my smoothest either as, in the event, I felt I was cramming a bit too much in. Dealing with the questions on the fly (more anxiety). Knew in advance it would be a long day by the the time the meeting was over at 6.30, so I didn't opt to drive back that evening. But it does mean that the next day is chewed into too. Rather bleak guest room. Then the hack back the next morning.

Benefits. Always nice to walk around Oxford. And a smart question (from Bruno Whittle) which might prompt a brief footnote in the reprint of the Gödel book.

Mmmm, the benefits are sure outweighed by the costs. So why on earth do I do these sorts of things? On the whole, I think I'll go back to my resolution to turn down all invitations except to very small workshops, which are the only occasions I tend to enjoy.

Thursday, February 21, 2008

Gödel book reprinting ...

I've just heard that the pbk of my Gödel book is almost sold out and there will be a reprint. I've got until the end of next week to make very minor corrections (so I'll correct a couple of dozen typos, and also correct the three more significant errors that I now know about). The reason for mentioning this is to encourage anyone who has been meaning to e-mail me corrections to please do so in the next few days!

Wednesday, February 20, 2008

Mathematics, Models and Modality

Another instalment in my continuing not-very-subtle campaign to bankrupt my readers by recommending unmissable books! I've just picked up from the CUP Bookshop a copy of John P. Burgess's new Mathematics, Models and Modality. It collects fourteen of his papers (mostly published before, though in very scattered places), with a useful introduction. Well worth having, and certainly your library should get a copy.

(But, having whet your appetite, I can perhaps save you some cash by noting that the new introduction and several papers are actually downloadable from Burgess's website, and most other papers you should be able to get online via your university's subscription to JSTOR.)

Monday, February 18, 2008

Logical Options, 5/6

I've put another (revised and expanded) instalment of my reading notes on Logical Options on-line here. Last week's and this week's seminars are on Section 3.1 on "Postulate systems", i.e. axiomatic theories. Again the notes have been dashed off pretty quickly, though helped by stealing a page or two from my Gödel book. Still, they might be useful to some students e.g. meeting the ideas of "models" and "categoricity" for the first time.

Friday, February 15, 2008

I wish I'd said that ...

A terrific remark by Louise Antony, writing on Ask Philosophers:

I'm the kind of atheist who thinks that God most respects people who apportion their beliefs to the evidence.

I wish I'd said that!

Wednesday, February 13, 2008

Asking another philosopher

I've admired the Ask Philosophers site for a while. The concept seems a brilliant one. And I've been much impressed by the quality of many of the responses from philosophers (not least, of course, from the sadly missed Peter Lipton) to the often inchoate questions sent in.

I was therefore genuinely pleased/flattered to get an email out of the blue a couple of days ago, asking if I'd like to join the panel of philosophers who contribute. So I said I'd be more than happy to give it a go (yes, yes, of course I need another excuse to procrastinate). You can see how I'm doing in my first three efforts here. I guess it will take me a while to hit the right note.

Talking of hitting the right note, you'd think, after decades of practice, I'd have nailed the business of giving intro logic lectures. But not so. I gave the last one of my course of 24 today -- a quick resume of where we've been (including a snappy outline of soundness/completeness for propositional trees), then a quick gesture at other ways of doing elementary logic (natural deduction), and pointers forward motivating second-year topics like modal logic and intuitionism. It was pretty action-packed and lively, though I say so myself, so it was very nice that the lectures finished on a high note and applause. But hacking through some of the stuff in the middle of the course wasn't so much fun this time around. Teaching someone else's textbook, you can fill up lectures enthusiastically "doing it better" (by your own lights). Teaching a book that you are in the middle of writing, you can explore to see what works well, and get immensely useful feedback on the drafts. But teaching my own textbook after publication, a book which isn't yet old enough for me to be wanting to do things very differently, is quite a bit trickier to get right, and this year I didn't. Oh well, roll on next academic year, and another shot at it!

Meanwhile, I've only seminars to give for the rest of this term, and then nothing until October as I'm on leave in the Easter term. Great. But I really must settle on what big project to take on next ... Watch this space.

Sunday, February 10, 2008

I must stop reading!

I'm trying to sort out my study at home a bit. Though "study" is a bit of a misnomer -- each time I've moved job it has been from a less expensive to a more expensive part of the country for housing, so where I used to have a beautiful large room overlooking the sea, I've now ended up in a little more than a book cupboard into which you can just squeeze a desk. That makes it all the more imperative to keep things tidy, and to chuck out books I no longer really want. Both of which I am terrible at.

But this time I have been trying much harder to reorganize the books, culling as I go. But it all takes so much time. Not just because I have to decide what to give to the library/students/Oxfam (though that's difficult enough). But I find it impossible not to keep stopping over a book I haven't opened in years and begin reading. I'm of the same mind as Churchill, who wrote

If you cannot read all your books, at any rate handle, or as it were, fondle them -- peer into them, let them fall open where they will, read from the first sentence that arrests the eye, set them back on the shelves with your own hands, arrange them on your own plan so that if you do not know what is in them, you at least know where they are. Let them be your friends; let them at any rate be your acquaintances. If they cannot enter the circle of your life, do not deny them at least a nod of recognition.

And those nods of recognition as I move the books from one shelf to another all take so much time!

Friday, February 08, 2008

Who knows what these ratings mean ...

... but in the "Education" section on blogged.com, Logic Matters is rated at no. 2 out of 883 "philosophy" blogs. Though on closer inspection they seem to have a pretty funny idea of what constitutes philosophy, and most of the best philosophy blogs aren't there on the list anyway. So I take this with a very big pinch of salt. Still I guess it has to be better than being ranked 882. And we're at no. 2 out of 83 maths blogs too. Gosh.

Mathematical Thought and Its Objects

I've only just noticed that Charles Parsons' long awaited book Mathematical Thought and Its Objects is due out this month here (and indeed has been out a few weeks in the US). From the CUP website:

Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a ‘nature’ than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
Obviously going to be a must-read.

Thursday, February 07, 2008

Seminar styles

I put some quick notes together for myself for the Hodges reading group yesterday: I'll work away at them again in the next few days (and certainly before the next seminar), and post the resulting after-the-event handout here, for it's worth [Later, this might take longer than I wanted]. I must say that the Hodges book is turning out to be harder going than I had imagined: he is capable elsewhere of writing about difficult stuff with verve and great clarity, but here things get a lot denser. I thought it might just be that my pure maths (group theory and the like) is rusty enough for me not to be getting enough out of some of the examples he gives: but then some mathmos have expressed similar views about his approachability.

A very noticeable difference in style is emerging between a logic reading group run for philosophers and one with a mixed group of philosophers, mathmos and compscis. Philosophers -- ok, our friendly local lot -- seem to be happy to share their ignorance, and take turns week-by-week to introduce a chapter or a paper, albeit fairly briefly, even if they make no pretence to really be on top of the stuff. And they will dive into the discussion, cheerfully asking for clarification, or trying out toy mini-examples, etc. Mathmos and compscis on the other hand -- although personally a perfectly friendly bunch! -- seem on the whole very reluctant to volunteer to have a bash at introducing a chapter, or indeed to say anything much after someone has given the intro. Which is a pity, as I learn a lot from the exchanges when they do happen.

Sunday, February 03, 2008

Logical Options, 4

For what they are worth, you can find my reading notes for next week's seminar on Sections 2.5 and 2.6 of Logical Options here (they might help some students). Writing these notes has very much been displacement behaviour in the last day or two: I should really be preparing something on Ch. 4 of the Shorter Hodges for the model theory seminar this week, which I daftly promised to introduce. But heavens, that is not exactly an easy read. Gulp.

Three cheers for Andy Clark

Thursday's Routledge Lecture here was given by Andy Clark. I thought he did a terrific job for a lecture intended for an audience not just of philosophers. I don't know if he is right or indeed if I fully understand what his position about the messiness of the mind comes to (and for once "I'm not sure I understand ..." is not philosopher-speak for "I'm damned sure he is horribly confused ..."). But I certainly think that he is concerned with a bunch of interesting issues, the kind of thing that is actually worth working on in the philosophy of mind -- engaging hands-on with the sciences of the mind.

I always thought of my old intro book with Owen Jones, The Philosophy of Mind, as an exercise in getting out of the way the relatively uninteresting a priori arm-chair stuff, kicking into touch various bits of mystery-mongering, leaving the field clear to get on with the interesting stuff engaging with work in cognitive neuro-psychology, artificial intelligence and the like. To be sure, we no doubt didn't get the a priori story dead right. But who really cares? We only need to get it, so to speak, right enough to enable us stop worrying that there might be mysterious obstacles in the way to a many-pronged empirically-informed assault on the interesting stuff. When I dip into the journals is a bit depressing to find in some areas epicycles of armchair reflection still being piled up by philosophers of mind. So three cheers for the likes of Andy Clark who remind us that it doesn't have to be that way.